Simplify 7x+3y-2+6x-1-y^2

i got the same question :D

Answer:

x ≥ -3

Step-by-step explanation:

i used a calculator, please give brainliest

It seems like the problem is asking for us to derive an expression for the force F⃗ stated in terms of the unit vectors i^ and j^.

The solution for this is:

U(x,y) = α (x^-2 + y^-2) 

F = - dU(x,y) 

F = - (dU/dx + dU/dy) 

F = - (-2αx^-3 - 2αy^-3) 

F = 2α (x^-3 + y^-3)

F = 2α (1/x^3 i + 1/y^3 j) 

A conservative force is related to the potential-energy function. In this particular context, the force exerted on an object in an xy-plane is calculated using the negative gradient of the potential energy function u(x,y) given.

The question presents a potential-energy function for an object moving in the xy-plane, with the function u(x,y)=α(1/x2+1/y2) where α is a positive constant. This case refers to the action of a conservative force.

A conservative force is characterized by the fact that the work done by the force is only dependent on the start and end points of the motion. In turn, this gives the freedom to define a potential energy for any conservative force. In the context of this potential-energy function, the conservative force acting on the object can be calculated from the negative gradient of the potential energy.

To express it quantitatively, given a potential energy function U(x), the force F acting on the object at a position x is given by F=-dU/dx. If we extend this to two dimensions in the xy-plane, the force F = - ∇U, where ∇ is the gradient operator.

Applying these concepts to your given potential energy function u(x,y)=α(1/x2+1/y2), the force acting on the object in the x and y directions can be calculated by differentiating this function with respect to x and y respectively, applying the opposite sign.

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Final answer:

By setting up and solving a system of equations, we find that there are 13 birds and 19 lions in the zoo.

Explanation:

To solve the problem of determining the number of birds and lions in the zoo given 32 heads and 102 feet, we can set up a system of equations. Birds have 2 feet, and lions have 4 feet. Let B represent the number of birds and L represent the number of lions.

Equations:

B + L = 32 (total heads)

2B + 4L = 102 (total feet)

Solving this system, we'll first multiply the first equation by 2 to facilitate elimination:

2B + 2L = 64

2B + 4L = 102

Subtracting the first modified equation from the second equation gives us 2L = 38, so L=19. Substituting L=19 into the first equation, we find B = 32 - 19 = 13.

Therefore, there are 13 birds and 19 lions in the zoo.

Graphing a parabola starts by identifying the vertex from the equation of the parabola, determining whether the parabola opens upwards or downwards, plotting the vertex and other points and then joining these points with a smooth curve.

Graphing a parabola involves understanding the equation of the parabola which takes the form y = ax² + bx + c, where 'a', 'b', and 'c' are constants. To find the graph of the parabola from this equation, follow these steps:

Remember, parabolas are a type of conic sections, formed through the intersection of a plane with a cone.

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The original price of the classic car was $5,000

The student's question seeks to determine the original price of a classic car, given that the selling price is $16,000, which is $1,000 more than three times its original price. To find the original price, we can set up an equation: let the original price be represented by x. The equation based on the information provided would be:

3x + $1000 = $16000

Subtracting $1000 from both sides to isolate the terms with x gives us:

3x = $16000 - $1000

3x = $15000

Finally, dividing both sides by 3 to solve for x, we get:

x = $15000 / 3

x = $5000

Therefore, the original price of the car was $5000.

The original price of the car was $5000

Let the original price of the car be  x.

According to the problem, the relationship between the original price and the selling price can be described by the following equation:

[tex]\[ 3x + 1000 = 16000 \][/tex]

To find x :

Isolate  x on one side :

  Subtract  1000 from both sides to remove the extra cost:

[tex]\[ 3x = 16000 - 1000 = 15000 \][/tex]

Solve for  x :

  Divide both sides by 3:

[tex]\[ x = \frac{15000}{3} = 5000[/tex]

Thus, the original price of the car was $5000.  

Question :  

The selling price for a classic car is $16000 which is. $1000 more than three times its original price. What was the original price of the car?

She has 4 nickels and 2 dimes

Let x represent the number of dimes

5+(x+2)+19x=40

5x+10x+10=40

15x=40-10

15x=30

x=30/15

x=2

x+2=4

Inconclusion She has 4 nickels and 2 dimes

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Step 1

Find the slope of the dotted line A

Let

[tex]A(-3,1)\\B(0,2)[/tex]

Find the slope m

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

substitute in the formula

[tex]m=\frac{(2-1)}{(0+3)}[/tex]

[tex]m=\frac{(1)}{(3)}[/tex]

[tex]mA=\frac{1}{3}[/tex]

Step 2

Find the equation of the line A

we know that

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]mA=\frac{1}{3}[/tex]

[tex]B(0,2)[/tex]

substitute

[tex]y-2=\frac{1}{3}(x-0)[/tex]

[tex]y=\frac{1}{3}x+2[/tex]

Step 3

Find the equation of the inequality A

we know that

the solution is below the dotted line A

so

the inequality A is    

[tex]y<\frac{1}{3}x+2[/tex]

Step 4

Find the slope of the solid line B

Let

[tex]B(0,2)\\C(1,0)[/tex]

Find the slope m

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

substitute in the formula

[tex]m=\frac{(0-2)}{(1-0)}[/tex]

[tex]m=\frac{(-2)}{(1)}[/tex]

[tex]mB=-2[/tex]

Step 5

Find the equation of the line B

we know that

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]mB=-2[/tex]

[tex]B(0,2)[/tex]

substitute

[tex]y-2=-2(x-0)[/tex]

[tex]y=-2x+2[/tex]

Step 6

Find the equation of the inequality B

we know that

the solution is below the solid line B

so

the inequality B is    

[tex]y\leq -2x+2[/tex]

therefore

The system of linear inequalities is

[tex]y<\frac{1}{3}x+2[/tex]

[tex]y\leq -2x+2[/tex]

using a graphing tool

the solution is the shaded area

see the attached figure

The boat average velocity for the one hour trip is 54° north of east.

What is Average velocity?

Average velocity is defined as the change in position divided by the time interval in which the displacement occurs.

Given that;

A small boat travel 32 km north and then travels 45 km east.

Now,

Average velocity is calculated as;

By figure,

Average velocity = cotθ = 32/45

θ = cot⁻¹ (32/45)

θ = 54°

Thus, The boat average velocity for the one hour trip is 54° north of east.

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110/154 = x/126

154x/13860

x = 13860 /154 = 90

 90 milligrams of medicine A

That point slope equation given does not pass through those points, the point slope equation y + 7 = -0.4(x - 10) does, though. The standard form of that would be 

2x + 5y = -15

You can get that by distributing the -0.4 out

y + 7 = -0.4x + 4

You can then add 0.4x to both sides, and subtract 7 from both sides to get

0.4x + y = -3

Now some teachers may accept this, but in correct standard form the coefficient of x is a whole number, so you have to multiply both sides by 5 to get rid of the decimal, and you get

A geometric sequence class in programming can represent a series of numbers where each term is generated by multiplying the previous term by a fixed number. This follows the rules of exponential arithmetic, as seen in examples of exponential increase and decrease.

In the context of programming, the basic framework of a geometric sequence class can represent a geometric sequence, following the rules of exponential arithmetic. In mathematics, a geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

For instance, a geometric sequence that begins at 1 and multiplies each term by 2 would look as follows: 1, 2, 4, 8, 16. Notice that each subsequent term is twice the value of its previous term i.e., an exponential increase.

Similarly, the geometric sequence 10.8, 5.4, 2.7, 1.35 starts at 10.8 and multiplies each term by 0.5, resulting in an exponential decrease. While not directly related to the question, geometric sequences can also be used to calculate geometric probabilities.

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The solution involves the application of mathematical properties such as the distributive property, the process of simplifying, the use of additive inverse, and the division property of equality. These steps result in x = 0.81.

To solve the given equation, 23x - 13 = 2(x + 2), let's break down the steps:

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To solve the equation 23x - 13 = 2(x + 2), distribute the 2, combine like terms, and isolate the variable x.

To solve the equation 23x - 13 = 2(x + 2), we need to simplify both sides of the equation step by step.

Therefore, the solution to the equation is x = 17/21.

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Tools of geometry consist of fundamental techniques and concepts in mathematics involving measurements, calculations, vectors, and moments of inertia among others. Active learning strategies like collaborative activities and problem-solving are effective in understanding these concepts.

The subject of your lesson, 'tools of geometry', refers to the fundamental concepts and techniques used in

Geometry

, which is a branch of mathematics concerned with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids. Some of these

tools

in geometry include the ability to measure and calculate length, mass, volume, density, temperature, and time, and to perform calculations and conversions in various unit systems. In geometry, you'll also find the concept of Moments of Inertia useful, this concept revolves around calculating the moment of inertia for uniformly shaped, rigid bodies and using the parallel axis theorem to find the moment of inertia about any particular axis. Geometry also involves vector analysis, where magnitudes have both direction and quantity, represented often in bold or with an arrow above them. A key aspect of learning geometry effectively is active participation through discussions, collaborative group activities, and hands-on problem-solving.

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The concept of percentages indicates that if Ramon answered 80% of the questions correctly in a test, it means he correctly answered a higher proportion of questions than the statement '30% of the students answered 16 or more questions correctly' would imply. Therefore, this statement does not represent the part of a test that Ramon answered correctly.

This question concerns the concept of percentages in mathematics. The information provided indicates that Ramon correctly answered 80% of the questions on his math test. This implies that if the test had 100 questions, Ramon correctly answered 80 questions. Now let's consider the statement in the choices: '30% of the students answered 16 or more questions correctly.' This is in stark contrast to Ramon's result and therefore does not represent the part of the test questions that Ramon answered correctly. The 30% statement is considering the entire class's performance, not Ramon's individual accomplishment. Hence, the aforementioned statement is the one that doesn't represent the part of the questions Ramon answered correctly.

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